In previous work~\cite{Dubins57, ReedsShepp90, SussmannTang91, SoueresLaumond96, SoueresBoissonnat98, BalkcomMason00}, the time optimal trajectories have been derived for three classes of non-holonomic mobile robots: steered cars that can only go forwards, steered cars that go forwards or backwards, and diff drives. Each of the vehicles is modelled as a rigid body in the plane, with velocity and angular velocity controls. The systems are differentiated only by the bounds on the controls, but the optimal trajectories are qualitatively different for each system. We explore this difference by considering the effect that control bounds have on the {\em extremal} trajectories of bounded velocity vehicles, where the {\em extremal} trajectories are defined to be the set of trajectories that satisfy Pontryagin's Maximum Principle, a necessary condition for optimality. To illustrate some of the similarities between bounded velocity vehicles, we develop some geometric interpretations of the Maximum Principle.